Gamow states as solutions of a modified Lippmann-Schwinger equation

Abstract

In this paper, we discuss the structure of Gamow states as solutions of Lippmann-Schwinger equation. The Friedrichs model is used to demonstrate it, both analytically and by applying perturbation theory to the extended spectrum of the Hamiltonian. The method presented here may be relevant to the inclusion of resonances in discrete basis, without the need of numerical constructions to define Gamow states, as entities depending on the choice of integrals contours, or as states resulting from ad hoc discretizations of the continuum.